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//! Verner Method Coefficient Verification Tests
//!
//! These tests verify that the Butcher tableau coefficients satisfy
//! the necessary order conditions for RK methods.
//!
//! Author: Moussa Leblouba
//! Date: 5 March 2026
//! Modified: 2 May 2026
#![allow(clippy::excessive_precision)]
#[cfg(test)]
mod tests {
// Import the tableau from the main crate
// We'll define the coefficients locally for testing
/// Vern7 coefficients from Jim Verner's website
mod vern7 {
pub const C: [f64; 10] = [
0.0,
0.005,
0.10888888888888888888888888888888888889,
0.16333333333333333333333333333333333333,
0.4555,
0.60950944899783813170870044214860249496,
0.884,
0.925,
1.0,
1.0,
];
pub const B: [f64; 10] = [
0.047155618486272221704317651088381756796,
0.0,
0.0,
0.25750564298434151895964361010376875810,
0.26216653977412620477138630957645277111,
0.15216092656738557403231331991651175355,
0.49399691700324842469071758932278768443,
-0.29430311714032504415572447440927034291,
0.081317472324951099997345994401367618925,
0.0,
];
pub const BHAT: [f64; 10] = [
0.044608606606341176287318175974791977814,
0.0,
0.0,
0.26716403785713726805091022609438378997,
0.22010183001772930199797157766507530963,
0.21884317031431568309831208335128938246,
0.22898717054112028833781738897635523654,
0.0,
0.0,
0.020295184663356282227670547938104303586,
];
}
/// Test: B weights sum to 1 (consistency condition)
#[test]
fn test_vern7_b_weights_sum() {
let sum: f64 = vern7::B.iter().sum();
assert!(
(sum - 1.0).abs() < 1e-14,
"Vern7 B weights sum = {} (should be 1)",
sum
);
}
/// Test: Bhat weights sum to 1 (consistency condition)
#[test]
fn test_vern7_bhat_weights_sum() {
let sum: f64 = vern7::BHAT.iter().sum();
assert!(
(sum - 1.0).abs() < 1e-14,
"Vern7 Bhat weights sum = {} (should be 1)",
sum
);
}
/// Test: First order condition Σbᵢ = 1
#[test]
fn test_vern7_order_condition_1() {
let sum: f64 = vern7::B.iter().sum();
assert!(
(sum - 1.0).abs() < 1e-14,
"Order 1 condition failed: Σbᵢ = {}",
sum
);
}
/// Test: Second order condition Σbᵢcᵢ = 1/2
#[test]
fn test_vern7_order_condition_2() {
let sum: f64 = vern7::B
.iter()
.zip(vern7::C.iter())
.map(|(b, c)| b * c)
.sum();
assert!(
(sum - 0.5).abs() < 1e-12,
"Order 2 condition failed: Σbᵢcᵢ = {} (should be 0.5)",
sum
);
}
/// Test: Third order condition Σbᵢcᵢ² = 1/3
#[test]
fn test_vern7_order_condition_3() {
let sum: f64 = vern7::B
.iter()
.zip(vern7::C.iter())
.map(|(b, c)| b * c * c)
.sum();
assert!(
(sum - 1.0 / 3.0).abs() < 1e-12,
"Order 3 condition failed: Σbᵢcᵢ² = {} (should be 1/3)",
sum
);
}
/// Test: Verify error coefficients E = B - Bhat
#[test]
fn test_vern7_error_coefficients() {
for i in 0..10 {
let expected_e = vern7::B[i] - vern7::BHAT[i];
// Just verify the values we computed are correct
println!("E[{}] = {}", i, expected_e);
}
}
/// Vern7 A matrix from Jim Verner's website (for row-sum verification)
mod vern7_a_matrix {
// Row i contains coefficients for stage i+1
// A[i][j] = a_{i+2, j+1} in standard notation
pub const A: [[f64; 9]; 9] = [
// Stage 2: a21 = 0.005
[0.005, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
// Stage 3: a31, a32
[
-1.076790123456790123456790123456790123457,
1.185679012345679012345679012345679012346,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
],
// Stage 4: a41, a42=0, a43
[
0.04083333333333333333333333333333333333333,
0.0,
0.1225,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
],
// Stage 5
[
0.6389139236255726780508121615993336109954,
0.0,
-2.455672638223656809662640566430653894211,
2.272258714598084131611828404831320283215,
0.0,
0.0,
0.0,
0.0,
0.0,
],
// Stage 6
[
-2.661577375018757131119259297861818119279,
0.0,
10.80451388645613769565396655365532838482,
-8.353914657396199411968048547819291691541,
0.8204875949566569791420417341743839209619,
0.0,
0.0,
0.0,
0.0,
],
// Stage 7
[
6.067741434696770992718360183877276714679,
0.0,
-24.71127363591108579734203485290746001803,
20.42751793078889394045773111748346612697,
-1.906157978816647150624096784352757010879,
1.006172249242068014790040335899474187268,
0.0,
0.0,
0.0,
],
// Stage 8
[
12.05467007625320299509109452892778311648,
0.0,
-49.75478495046898932807257615331444758322,
41.14288863860467663259698416710157354209,
-4.461760149974004185641911603484815375051,
2.042334822239174959821717077708608543738,
-0.09834843665406107379530801693870224403537,
0.0,
0.0,
],
// Stage 9
[
10.13814652288180787641845141981689030769,
0.0,
-42.64113603171750214622846006736635730625,
35.76384003992257007135021178023160054034,
-4.348022840392907653340370296908245943710,
2.009862268377035895441943593011827554771,
0.3487490460338272405953822853053145879140,
-0.2714390051048312842371587140910297407572,
0.0,
],
// Stage 10 (used for bhat only, not in main 7th order solution)
[
-45.03007203429867712435322405073769635151,
0.0,
187.3272437654588840752418206154201997384,
-154.0288236935018690596728621034510402582,
18.56465306347536233859492332958439136765,
-7.141809679295078854925420496823551192821,
1.308808578161378625114762706007696696508,
0.0,
0.0,
],
];
}
/// Test: Row sum condition - c[i] = sum(A[i][j])
#[test]
fn test_vern7_row_sum_condition() {
for i in 0..9 {
let row_sum: f64 = vern7_a_matrix::A[i].iter().sum();
let expected_c = vern7::C[i + 1]; // c[i+1] for stage i+2
assert!(
(row_sum - expected_c).abs() < 1e-10,
"Row {} sum = {} ≠ c[{}] = {}",
i + 2,
row_sum,
i + 1,
expected_c
);
}
}
/// Integration test: Solve exponential decay with Vern7
#[test]
fn test_vern7_exponential_decay() {
use numra_ode::{OdeProblem, Solver, SolverOptions, Vern7};
let problem = OdeProblem::new(
|_t, y: &[f64], dydt: &mut [f64]| {
dydt[0] = -y[0];
},
0.0,
2.0,
vec![1.0],
);
let options = SolverOptions::default().rtol(1e-6).atol(1e-8);
let result = Vern7::solve(&problem, 0.0, 2.0, &[1.0], &options).unwrap();
assert!(result.success, "Vern7 should succeed");
let y_final = result.y_final().unwrap();
let expected = (-2.0_f64).exp();
println!("Vern7 result: {}, expected: {}", y_final[0], expected);
println!(
"Relative error: {}",
(y_final[0] - expected).abs() / expected
);
// For a 7th order method with rtol=1e-6, expect very good accuracy
// Actual relative error is ~1.5e-8; use 1e-5 for comfortable margin
assert!(
(y_final[0] - expected).abs() < expected * 1e-5,
"Vern7 result {} differs from expected {} by more than 1e-5 relative",
y_final[0],
expected
);
}
}